## Strong meager properties for filters

### Abstract

We analyze several strong meager'' properties for filters on the natural numbers between the classical Baire property and a filter being $F_\sigma$. Two such properties have been studied by Talagrand and a few more combinatorial ones are investigated. In particular, we define the notion of a P$^+$-filter, a generalization of the traditional concept of P-filter, and prove the existence of a non-meager P$^+$-filter. Our motivation lies in understanding the structure of filters generated by complements of members of a maximal almost disjoint family

Topics: Mathematics - Logic
Year: 1993
OAI identifier: oai:arXiv.org:math/9312204

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